NEW DELHI—Hundreds of people showed up at an auditorium in India’s capital on Thursday for a surprisingly passionate hourslong debate over whether Facebook and others are undermining freedom of the Internet by offering free services that give people limited access to the web.

Representatives of India’s cellular service operators joined net-neutrality activists, startup executives and regular Internet users for an open-house discussion hosted by the Telecom Regulatory Authority of India. The discussion centered on the…